Hard scale dependent gluon density, saturation and forward-forward dijet production at the LHC

Abstract

We propose a method to introduce Sudakov effects to the unintegrated gluon density promoting it to be hard scale dependent. The advantage of the approach is that it guarantees that the gluon density is positive definite and that the Sudakov effects cancel on integrated level. As a case study we apply the method to calculate angular correlations and $R_{pA}$ ratio for p+p vs. p+Pb collision in the production of forward-forward dijets.

Figures (3)

• Figure 1: We abbreviate unintegrated gluon density by UGD. Left: unintegrated gluon density of proton with Sudakov effects evaluated at $x=10^{-5}$ at hard scale $\mu^2=20GeV^2$ (continuous red line), hard scale $\mu^2=200GeV^2$ (purple dotted line), unintegrated gluon density without Sudakov effects evaluated at $x=10^{-5}$ (blue dashed line). Right: unintegrated gluon density of Pb with Sudakov effects evaluated at $x=10^{-5}$ at hard scale $\mu^2=20GeV^2$ (continuous red line), hard scale $\mu^2=200GeV^2$ (purple dotted line), unintegrated gluon density without Sudakov effects evaluated at $x=10^{-5}$ (blue dotted line)
• Figure 2: Left: cross section for decorelations in production of forward-forward dijet in p+p collision at $7\,TeV$. The rapidities of produced jets satisfy $p_{t1}\!>\!p_{t2}>20 GeV$. The continuous red line corresponds to the situation with Sudakov effects included while the blue dashed line omits Sudakov effects. Right: the $R_{pA}$ ratio for p+p v. p+Pb. The continuous red line corresponds to situation with Sudakov effects included while the blue dashed line omits Sudakov effects, the brown line just helps to see the deviation from unity.
• Figure 3: Left: ratio of unintegrated gluon density (UGD) of lead to unintegrated gluon density of proton evaluated at $x=10^{-3}$ at hard scale $\mu^2=25GeV^2$(green dotted line), $\mu^2=45GeV^2$ (purple dashed line), $\mu^2=80GeV^2$ (magenta dotted line), $\mu^2=400GeV^2$ (red continuous line), no hard scale dependence (blue dashed line). Right: ratio of gluon density of lead to gluon density of proton evaluated at $x=10^{-5}$ at hard scale $\mu^2=25GeV^2$(green dotted line), $\mu^2=45GeV^2$ (purple dashed line), $\mu^2=80GeV^2$ (magenta dotted line), $\mu^2=400GeV^2$ (red continuous line), no hard scale dependence (blue dashed line)